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            <h1 id="seo-header">深度优先搜索-DFS</h1>
            
              <p id="updated-time" class="note note-info" style="">
                
                  
                    本文最后更新于 2025年3月17日 晚上
                  
                
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                <h1 id="栈">栈</h1>
<h2 id="特点">特点</h2>
<p>栈是后进先出（Last In First Out）的线性表，简称LIFO表</p>
<p><img src="Snipaste_2022-12-13_23-49-18.png" srcset="/img/loading.gif" lazyload /></p>
<h2 id="例子">例子</h2>
<h3 id="迷宫最短路问题">迷宫最短路问题</h3>
<p>这个问题实际上使用DFS和BFS都可以实现,而且就找最短路来说，队列的时间复杂度更小，但是为了符合回溯这个主题，我们尝试使用DFS来做。</p>
<h4 id="原理">原理</h4>
<pre><code class="hljs">每走一次就入栈一次，每一次都走到无路可走或走到终点时退栈，找下一条路。</code></pre>
<h4 id="代码">代码</h4>
<figure class="highlight c"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span 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class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br><span class="line">103</span><br><span class="line">104</span><br><span class="line">105</span><br><span class="line">106</span><br><span class="line">107</span><br><span class="line">108</span><br><span class="line">109</span><br><span class="line">110</span><br><span class="line">111</span><br><span class="line">112</span><br><span class="line">113</span><br><span class="line">114</span><br><span class="line">115</span><br><span class="line">116</span><br><span class="line">117</span><br><span class="line">118</span><br><span class="line">119</span><br><span class="line">120</span><br><span class="line">121</span><br><span class="line">122</span><br><span class="line">123</span><br><span class="line">124</span><br><span class="line">125</span><br><span class="line">126</span><br><span class="line">127</span><br><span class="line">128</span><br><span class="line">129</span><br><span class="line">130</span><br><span class="line">131</span><br><span class="line">132</span><br><span class="line">133</span><br><span class="line">134</span><br><span class="line">135</span><br></pre></td><td class="code"><pre><code class="hljs c"><span class="hljs-meta">#<span class="hljs-keyword">include</span><span class="hljs-string">&lt;stdio.h&gt;</span></span><br><span class="hljs-meta">#<span class="hljs-keyword">include</span><span class="hljs-string">&lt;windows.h&gt;</span></span><br><span class="hljs-type">char</span> ch[<span class="hljs-number">10</span>][<span class="hljs-number">10</span>];<br><span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">pos</span>&#123;</span><br>    <span class="hljs-type">int</span> dir;<br>    <span class="hljs-type">int</span> row;<br>    <span class="hljs-type">int</span> col;<br>&#125;poss[<span class="hljs-number">101</span>];<br><span class="hljs-class"><span class="hljs-keyword">struct</span> <span class="hljs-title">pos</span> <span class="hljs-title">res</span>[101];</span><br><span class="hljs-comment">//入栈</span><br><span class="hljs-type">void</span> <span class="hljs-title function_">forward</span><span class="hljs-params">(<span class="hljs-type">int</span>* row, <span class="hljs-type">int</span>* col, <span class="hljs-type">int</span>* type)</span><br>&#123;<br>	<span class="hljs-comment">//这里运用了二进制减少变量</span><br>    <span class="hljs-keyword">if</span> (*type &amp; <span class="hljs-number">1</span>)ch[*row][++ * col] = <span class="hljs-string">&#x27;@&#x27;</span>, * type ^= <span class="hljs-number">1</span>;<br>    <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (*type &amp; <span class="hljs-number">2</span>)ch[++ * row][*col] = <span class="hljs-string">&#x27;@&#x27;</span>, * type ^= <span class="hljs-number">2</span>;<br>    <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (*type &amp; <span class="hljs-number">4</span>)ch[*row][-- * col] = <span class="hljs-string">&#x27;@&#x27;</span>, * type ^= <span class="hljs-number">4</span>;<br>    <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (*type &amp; <span class="hljs-number">8</span>)ch[-- * row][*col] = <span class="hljs-string">&#x27;@&#x27;</span>, * type ^= <span class="hljs-number">8</span>;<br>&#125;<br><span class="hljs-type">void</span> <span class="hljs-title function_">print</span><span class="hljs-params">()</span><br>&#123;<br>    <span class="hljs-keyword">for</span> (<span class="hljs-type">int</span> i = <span class="hljs-number">0</span>; i &lt; <span class="hljs-number">10</span>; i++) &#123;<br>        <span class="hljs-keyword">for</span> (<span class="hljs-type">int</span> j = <span class="hljs-number">0</span>; j &lt; <span class="hljs-number">10</span>; j++) &#123;<br>            <span class="hljs-built_in">printf</span>(<span class="hljs-string">&quot;%c &quot;</span>, ch[i][j]);<br>        &#125;<br>        <span class="hljs-built_in">printf</span>(<span class="hljs-string">&quot;\n&quot;</span>);<br>    &#125;<br>    <span class="hljs-keyword">return</span>;<br>&#125;<br><span class="hljs-type">int</span> <span class="hljs-title function_">judge</span><span class="hljs-params">(<span class="hljs-type">int</span> row, <span class="hljs-type">int</span> col,<span class="hljs-type">int</span> tmp)</span><br>&#123;<br>    <span class="hljs-type">int</span> f = <span class="hljs-number">0</span>;<br>    poss[tmp].col = col;<br>    poss[tmp].row = row;<br>    <span class="hljs-keyword">if</span> (col + <span class="hljs-number">1</span> &lt; <span class="hljs-number">10</span> &amp;&amp; ch[row][col + <span class="hljs-number">1</span>] == <span class="hljs-string">&#x27; &#x27;</span>)poss[tmp].dir += <span class="hljs-number">1</span>, f = <span class="hljs-number">1</span>;<br>    <span class="hljs-keyword">if</span> (col - <span class="hljs-number">1</span> &gt;= <span class="hljs-number">0</span> &amp;&amp; ch[row][col - <span class="hljs-number">1</span>] == <span class="hljs-string">&#x27; &#x27;</span>)poss[tmp].dir += <span class="hljs-number">4</span>, f = <span class="hljs-number">1</span>;<br>    <span class="hljs-keyword">if</span> (row + <span class="hljs-number">1</span> &lt; <span class="hljs-number">10</span> &amp;&amp; ch[row + <span class="hljs-number">1</span>][col] == <span class="hljs-string">&#x27; &#x27;</span>)poss[tmp].dir += <span class="hljs-number">2</span>, f = <span class="hljs-number">1</span>;<br>    <span class="hljs-keyword">if</span> (row - <span class="hljs-number">1</span> &gt;= <span class="hljs-number">0</span> &amp;&amp; ch[row - <span class="hljs-number">1</span>][col] == <span class="hljs-string">&#x27; &#x27;</span>)poss[tmp].dir += <span class="hljs-number">8</span>, f = <span class="hljs-number">1</span>;<br>    <span class="hljs-keyword">return</span> f;<br>&#125;<br><span class="hljs-type">int</span> <span class="hljs-title function_">main</span><span class="hljs-params">()</span><br>&#123;<br>    <span class="hljs-type">int</span> startr, startc;<br>    <span class="hljs-type">int</span> endr, endc;<br>    <span class="hljs-type">int</span> min=<span class="hljs-number">0</span>;<br>    <span class="hljs-keyword">for</span> (<span class="hljs-type">int</span> i = <span class="hljs-number">0</span>; i &lt; <span class="hljs-number">10</span>; i++) &#123;<br>        <span class="hljs-keyword">for</span> (<span class="hljs-type">int</span> j = <span class="hljs-number">0</span>; j &lt; <span class="hljs-number">10</span>; j++) &#123;<br>            <span class="hljs-built_in">scanf</span>(<span class="hljs-string">&quot;%c%*c&quot;</span>, &amp;ch[i][j]);<br>            <span class="hljs-comment">//起点</span><br>            <span class="hljs-keyword">if</span> (ch[i][j] == <span class="hljs-string">&#x27;@&#x27;</span>) &#123;<br>                startr = i; startc = j;<br>            &#125;<br>            <span class="hljs-comment">//终点</span><br>            <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (ch[i][j] == <span class="hljs-string">&#x27;*&#x27;</span>) &#123;<br>                endr = i; endc = j;<br>                ch[i][j] = <span class="hljs-string">&#x27; &#x27;</span>;<br>            &#125;<br>        &#125;<br>    &#125;<br>    system(<span class="hljs-string">&quot;cls&quot;</span>);<br>    print();<br>    Sleep(<span class="hljs-number">500</span>);<br>    <span class="hljs-type">int</span> tmp = <span class="hljs-number">0</span>;<br>    <span class="hljs-keyword">while</span> (<span class="hljs-number">1</span>) &#123;<br>        <span class="hljs-type">int</span> f = judge(startr, startc, tmp);<br>        system(<span class="hljs-string">&quot;cls&quot;</span>);<br>        forward(&amp;startr, &amp;startc, &amp;poss[tmp].dir);<br>        print();<br>        Sleep(<span class="hljs-number">500</span>);<br>        <span class="hljs-keyword">if</span> (startr == endr &amp;&amp; startc == endc) &#123;<br>            <span class="hljs-comment">//记录最短路</span><br>            <span class="hljs-keyword">if</span> (min == <span class="hljs-number">0</span>) &#123;<br>                min = tmp + <span class="hljs-number">1</span>;<br>                <span class="hljs-keyword">for</span> (<span class="hljs-type">int</span> k = <span class="hljs-number">0</span>; k &lt; min; k++)res[k] = poss[k];<br>                res[min].row = endr;<br>                res[min].col = endc;<br>            &#125;<br>            <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (min &gt; tmp)&#123;<br>	            min = tmp+<span class="hljs-number">1</span>;<br>	            <span class="hljs-keyword">for</span> (<span class="hljs-type">int</span> k = <span class="hljs-number">0</span>; k &lt; min; k++)res[k] = poss[k];<br>                res[min].row = endr;<br>                res[min].col = endc;<br>            &#125;<br>            ch[endr][endc] = <span class="hljs-string">&#x27; &#x27;</span>;<br>            <span class="hljs-keyword">while</span> (poss[tmp].dir == <span class="hljs-number">0</span> &amp;&amp; tmp &gt;= <span class="hljs-number">0</span>)&#123; <br>                ch[poss[tmp].row][poss[tmp].col] = <span class="hljs-string">&#x27; &#x27;</span>;<br>                tmp--;<br>                system(<span class="hljs-string">&quot;cls&quot;</span>);<br>                print();<br>                Sleep(<span class="hljs-number">100</span>);<br>            &#125;<br>            <span class="hljs-keyword">if</span> (tmp &lt; <span class="hljs-number">0</span>) &#123;<br>                <span class="hljs-comment">//输出最短路</span><br>                <span class="hljs-keyword">for</span> (<span class="hljs-type">int</span> i = <span class="hljs-number">0</span>; i &lt;= min; i++) &#123;<br>			        ch[res[i].row][res[i].col] = <span class="hljs-string">&#x27;@&#x27;</span>;<br>			    &#125;<br>			    system(<span class="hljs-string">&quot;cls&quot;</span>);<br>			    print();<br>                <span class="hljs-built_in">printf</span>(<span class="hljs-string">&quot;%d&quot;</span>,min);<br>                <span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;<br>            &#125;<br>            startr = poss[tmp].row;<br>            startc = poss[tmp].col;<br>            forward(&amp;startr, &amp;startc, &amp;poss[tmp].dir);<br>            system(<span class="hljs-string">&quot;cls&quot;</span>);<br>            print();<br>            Sleep(<span class="hljs-number">500</span>);<br>        &#125;<br>        <span class="hljs-keyword">else</span> <span class="hljs-keyword">if</span> (f == <span class="hljs-number">0</span>) &#123;<br>        <span class="hljs-keyword">while</span> (poss[tmp].dir == <span class="hljs-number">0</span> &amp;&amp; tmp &gt;= <span class="hljs-number">0</span>)&#123;<br>            ch[poss[tmp].row][poss[tmp].col] = <span class="hljs-string">&#x27; &#x27;</span>;<br>            tmp--;<br>            system(<span class="hljs-string">&quot;cls&quot;</span>);<br>            print();<br>            Sleep(<span class="hljs-number">100</span>);<br>            &#125;<br>            <span class="hljs-keyword">if</span> (tmp &lt; <span class="hljs-number">0</span>) &#123;<br>	            <span class="hljs-comment">//输出最短路</span><br>	            <span class="hljs-keyword">for</span> (<span class="hljs-type">int</span> i = <span class="hljs-number">0</span>; i &lt;= min; i++) &#123;<br>			        ch[res[i].row][res[i].col] = <span class="hljs-string">&#x27;@&#x27;</span>;<br>			    &#125;<br>			    system(<span class="hljs-string">&quot;cls&quot;</span>);<br>			    print();<br>                <span class="hljs-built_in">printf</span>(<span class="hljs-string">&quot;%d&quot;</span>,min);<br>                <span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;<br>            &#125;<br>            startr = poss[tmp].row;<br>            startc = poss[tmp].col;<br>            forward(&amp;startr, &amp;startc, &amp;poss[tmp].dir);<br>            system(<span class="hljs-string">&quot;cls&quot;</span>);<br>            print();<br>            Sleep(<span class="hljs-number">500</span>);<br>        &#125;<br>        tmp++;<br>    &#125;<br>&#125;<br></code></pre></td></tr></table></figure>
<h4 id="输入实例">输入实例</h4>
<figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br></pre></td><td class="code"><pre><code class="hljs input"># # #   # #   # # #<br># @               #<br># #   # # # # #   #<br>#                 #<br># #   # # #   #   #<br># #   #   #   #   #<br># #   #   #   #   #<br># #       #   #   #<br># # # # # #   #   #<br># # # # # # * #   #<br></code></pre></td></tr></table></figure>
<p>其实可以发现上面的很多代码都是重复的，主要是因为我们不是只要找到一条通向终点的路，而是要找到最短路，所以我们要将所有的路都走一遍。</p>

                
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